Ensure that you have copied/back up all of the info that you need, as you're about to delete it all. Don't forget the contents of email accounts and bookmarks of all browsers as well as the obvious docs, music and pics.

Log out of your current user account and log back in under the new Spare account.

In the Accounts System Preference, select the user account that you want to delete and click on the - (minus) symbol under the list of users. Choose the delete option, and go and make tea - it may take up to 30 mins to finish deleting, if you had a lot of data.

Note that you won't have deleted the third-party apps that are installed, such as Photoshop etc, so decide whether you want to keep the discs and pass on the installed copies to the new owner (illegal), or either pass on the discs and licence keys, or delete the installed copies and keep the discs and licence keys for your new Mac (legal).